MHB Does the Intermediate Value Theorem Apply If h(a) and h(b) Have Opposite Signs?

TheDougheyMan · Apr 2, 2014

I have a continuous function h(x) and the inequality h(b)<=0<=h(a). Can I apply IVT?

Ackbach · Apr 2, 2014

Well, what are the hypotheses of the IVT? Are they satisfied in your case?

TheDougheyMan · Apr 2, 2014

Ackbach said:

Well, what are the hypotheses of the IVT? Are they satisfied in your case?

Isn't it just that h(x) is continuous and if u is a number between h(b) and h(a),
h(b) < u < h(a), then etc etc. I didn't think I could, but I just wanted to see a variation of it.

Ackbach · Apr 2, 2014

TheDougheyMan said:

Isn't it just that h(x) is continuous and if u is a number between h(b) and h(a),
h(b) < u < h(a), then etc etc. I didn't think I could, but I just wanted to see a variation of it.

Exactly right. So you can conclude that there is a $c \in (a,b)$ (I'm assuming $a<b$) such that $h(c)=0$.

MHB Does the Intermediate Value Theorem Apply If h(a) and h(b) Have Opposite Signs?

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